OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 9*n - a(n-1) - 6, n>1.
a(n) = 3*A168236(n). - R. J. Mathar, Jul 10 2011
G.f. 3*x*(2 + x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 10 2011
a(n) = 6 + 9*Floor((n-1)/2). - Vincenzo Librandi, Sep 19 2013
From G. C. Greubel, Jul 22 2016: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3).
E.g.f.: (3/4)*(-3 + 4*exp(x) +(6*x - 1)*exp(2*x))*exp(-x). (End)
MATHEMATICA
Table[6 + 9 Floor[(n - 1)/2], {n, 70}] (* or *) CoefficientList[Series[3 (2 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)
LinearRecurrence[{1, 1, -1}, {6, 6, 15}, 60] (* Harvey P. Dale, May 17 2017 *)
PROG
(Magma) [6+9*Floor((n-1)/2): n in [1..70]]; // Vincenzo Librandi, Set 19 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 25 2009
EXTENSIONS
Definition replaced by Lava formula of Nov 2009. - R. J. Mathar, Jul 10 2011
STATUS
approved